Problem: A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$5.00$, and bags of cookies cost $$4.50$, and sales equaled $$47.00$ in total. There were $2$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${5x+4.5y = 47}$ ${y = x+2}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+2}$ for $y$ in the first equation. ${5x + 4.5}{(x+2)}{= 47}$ Simplify and solve for $x$ $ 5x+4.5x + 9 = 47 $ $ 9.5x+9 = 47 $ $ 9.5x = 38 $ $ x = \dfrac{38}{9.5} $ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $ {y = x+2}$ to find $y$ ${y = }{(4)}{ + 2}$ ${y = 6}$ You can also plug ${x = 4}$ into $ {5x+4.5y = 47}$ and get the same answer for $y$ ${5}{(4)}{ + 4.5y = 47}$ ${y = 6}$ $4$ bags of candy and $6$ bags of cookies were sold.